c) Linear equations At node 11, the beam is pushed towards negative x; thus, the effective force at 11 is negative. a) x=N1x1+N2x2 What is the total size of the assembled stiffness matrix of a plane elastic structure such that its finite element mesh has eight nodes and two degrees of freedom at each node? b) One degree of freedom b) Upper triangular matrix Which is considered good practice concerning the a) Stiffness matrix A. occurring perpendicular to the direction of the beam. Here NBW=____ Explanation: Stress is defined as force per unit area. How many nodes are there in a hexahedron element? The Cutometer applies a vacuum to the skin and measures the extent to which it can be vertically distended. d) uTTl After determining the stresses in orthotropic materials by using an appropriate failure theory we can find factor of safety. These measurements are able to distinguish between healthy skin, normal scarring, and pathological scarring,[5] and the method has been applied within clinical and industrial settings to monitor both pathophysiological sequelae, and the effects of treatments on skin. Answer: c 7-15 AMA037 Stress- strain law defined as ______ Here is the workflow for obtaining the stiffness from the 1D model: A snapshot of the 1D model made using the Beam interface. The other end is supported by roller and hinge support. c) Both Precision and accuracy By signing up, you agree to our Terms of Use and Privacy Policy. b) Thermo couple Explanation: A state of plane stress in XYZ Cartesian system is defined as one in which the following stress field exists: Is stiffness the same as elasticity matrix? Crack propagation problems come under this category. b) Hole Common problems are as follows: Poisson's Ratio of 0.5. Mar 20, 2022. d) Body force, Traction force & Point load Discretization includes both node and element numbering, in this model every element connects two nodes. Answer: d c) Lower triangular matrix b) Constant 32. C. dirt and foreign substances from between The geometric deformation increases with the square of the rotation of the element. d) A1 35. Is there any spatial inhomogeneity in the material properties? This load vector is obtained by due to given load. Arjan82. b) KeKe b) Load c) Computer program Explanation: Traction or tractive force is the force used to generate motion between a body and a tangential surface, through the use of dry friction, through the use of shear force of the surface. B.19. 6.3 Aircraft Materials - Composite and Non-Me, 6.3 Aircraft Material - Composite and Non-met. b) Penalty approach a) Entire body Engines). Answer: a b) x-, co-ordinates Our first formula defines the deflection of a cantilever beam with a load at one end. Which is true regarding the use of polymerizable cements We can see that the deflection is 0.0646, which is pretty close to our spreadsheet calculations again. In COMSOL Multiphysics, you can model the 0D case using the Global ODEs and DAEs interface (for time-dependent simulations) or by simply setting up Parameters or Variables in a 0D space dimension model. Explanation: Poissons ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. Which technique do traditional workloads use? Write the element stiffness for a truss element. a) Surface c) -, y- co-ordinates Answer: a c) Radially Last edited on 25 February 2023, at 17:23, "Collagen-Based Biomaterials for Wound Healing", https://en.wikipedia.org/w/index.php?title=Stiffness&oldid=1141556857, torsional stiffness - the ratio of applied, This page was last edited on 25 February 2023, at 17:23. Use of quadratic interpolation leads to more accurate results. d) Cannot be determined 14. Here B is element strain displacement matrix. d) 4 33. The notches are causing in a homogeneous stress distribution, as notches fillets are also a cause for in homogenous stress distribution. C. install anchor tabs on the aluminum surface. of nodes*Degrees of freedom per node b) Accuracy This article is part one of a two-part series that discusses different methods for increasing part stiffness. A. is lighter than single sheet skin of the same strength Then elemental volume is given by c) Six degrees of freedom b) Boundary conditions c) N1=0 & N2=x Use of linear shape functions results in a constant B matrix. Stiffness matrix depends on [A] material [B] geometry [C] both The sub domains are called as [A] particles [B] molecules [C] elements . a) No. The images below illustrate the critical dimensions for impacting part stiffness. a) A1/A 2. remove water from damage area. In a constant strain triangle, element body force is given as ____. c) Y direction B. fasteners and metal structure fasteners is that d) Augmented matrix. Explanation: By penalty approach we can derive boundary conditions of an element or a structure. Strain is response of a system t an applied stress. So your stiffness matrix will be 8x8. c) Non symmetric and rectangular Explanation: The plane strain problems are characterized by the displacement field ux=ux(x,y), uy=uy(x,y) and uz=0, where (ux, uy, uz) denote the components of this displacement vector u in the (x, y, z) coordinate system. 1. remove the damage. Each node is subjected to two degrees of freedom (figure 3a) and 2 nodal forces (figure 3b). In other words, Fictiv lets engineers, like you, engineer. a) xy=0 Next up, we will talk about 2D and 3D cases. 7-28 AMA037 Answer: b b) Load Answer: c This gives us two possible equivalent single-spring bending stiffnesses of the 1D beam depending on the loading direction. [1], The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. hWko6H l'N8ieVI~lbh.8vqkv]}u8t#19X:Lx!PI4[i^fPNvvhNE{{vAWZjovgW94aVU]Ncu}E^7.~hfqWIQ7:A$4"8i8b;8bj|fSUV{g*O$.gIn{EeHWE%t7#:#2RNS)Rp3*+V3UhfCB& ^$v4yM1gQhL;tJ'.O#A_hG[o '~K&^?^m-)V;mfIEv(FN9Tq;8UAQ'%"UyAj{{<4";f|dcLNV&~? b) Rayleigh method A. high speed, low pressure drills. The purpose of a double vacuum de-bulk process when The gussets are added to increase the part stiffness and strength, but how do we calculate this without extensive hand calculations? This would require us to solve the following moment-balance equation: and at x=L; \frac{d^2w}{dx^2}=0 and -EI\frac{d^3w}{dx^3}=F. Explanation: The finite element method is a numerical method for solving problems of engineering and mathematical physics. ; Note that the torsional stiffness has dimensions [force] * [length] / [angle], so that its SI units are N*m/rad. Answer: b C. firm fit. 2. Explanation: In mathematics, a volume element provides a means for integrating a function with respect to volume in various co-ordinate systems such as spherical co-ordinates and cylindrical co-ordinates. a) Row vector 16. For example, lets look at a boss with gussets (below) similar to what I described in a previous article. 15. As shown here, you can create a switch using the if() operator and the names (such as root.group.lg1) associated with the Load Groups, such that only one component of the force vector can be made nonzero at a time when you are solving the same model for several load cases. a) Large circular sections B. static electrical buildup. Element boundaries are defined when nodal points are connected by unique polynomial curve or surface. Answer: b The stiffness matrix is an inherent property of the structure. point of the heat source. He was told about his Gleason score but is not sure what this is. b) Element strain energy Using a simplistic definition where stress is equal to force per unit cross-section area, \sigma=F/A, where A=bt, and strain is equal to the ratio of deformation to the original length, \epsilon=u/L, and combining these, we get F=(EA/L)u. d) Shrinking technique c) Z direction Potential energy =1/2[QTKQ-QTF]. d) No traction force The principal material axes that are normal to the _______ Answer: b Material Geometry both material and geometry none of the above Answer: both material and geometry For 1-D bar elements if the structure is having 3 nodes then the 13. stiffness matrix formed is having an order of 2*2 3*3 4*4 6*6 Answer: 3*3 When thin plate is subjected to loading in its own plane only, {\displaystyle k,} d) Both shape functions and co-ordinate functions 1. c) Non symmetric Explanation: The finite element method is a numerical method for solving problems of engineering and mathematical physics. If an aircraft's transparent plastic enclosures exhibit fine Body forces contrast with contact forces or the classical definition of surface forces which are exerted to the surface of the object. Global stiffness K is a______ matrix. Explanation: The stiffness matrix represents system of linear equations that must be solved in order to ascertain an approximate solution to differential equation. Answer: a to use d) Uniform strains , b) Iterative equations Shape function is just a ___________ pressure system to absorb excess resin during curing called? 150 degrees 3. install the honeycomb core and repair plies. Answer: b If N3is dependent shape function, It is represented as ____ ultrasonic monitoring This consent may be withdrawn. In this case, a 0D model is also a single degree of freedom (SDOF) representation of the beam. Answer: d Explanation: The size of the assembled stiffness matrix is equal to the total DOF of a structure. b) Rayleigh method Explanation: In finite element modeling, each element connects to 2 nodes. Explanation: The basic procedure for a one dimensional problem depends upon total potential energy, stress-strain relation and strain-displacement relation are used in developing the finite element modeling. C. When nuts and bolts are used, the plastic should i am doing uniaxial compression test simulation of polymer (ABS material ). / A category of plastic material that is capable of softening or k Today, stiffness usually refers to the finite element stiffness matrix, which can include all of the above stiffness terms plus general solid or shell . https://quizack.com/mechanical-engineering/finite-element-method/mcq/stiffness-matrix-depends-on, Note: This Question is unanswered, help us to find answer for this one, More Mechanical Engineering MCQ Questions, The force required to produce unit displacement is, The distributed force per unit area on the surface of the body is, Domain is divided into some segments called, Unit of body force acting on every elemental volume of the body is, ________ are used to find the nodal displacements in all parts of element. Even the simplest designs can be sensitive to part stiffness. Under plane stress condition in the XYZ Cartesian system, which stress value is correct if a problem is characterized by the stress field xx=xx(x,y), yy=yy(x,y) and zz=0? The distribution of change in temperature, the strain due to this change is initial strain. He is planning to have surgery in 2 weeks but is concerned about the possible consequences of surgery. Explanation: The displacement components of a local node is represented in x and y directions, respectively. Under such a condition, the above equation can obtain the direct-related stiffness for the degree of unconstrained freedom. Explanation: The given equation is Element strain energy equation. b) Skew symmetric matrix. A. cure the film adhesive material at 250 degrees F. A rich library of design guides and manufacturing tips. Deformation at the end of elements are called _____________ Answer: a Answer: a A features shape and size impact the formulas required for a calculation of stiffness, so lets consider those geometric properties first. Having mastered the art of modifying part stiffness using a geometric approach, you may need to source a supplier to manufacture your expertly designed parts. 21. I have a question. Answer: c Explanation: Stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. a) Interpolation function d) Symmetric and rectangular When installing transparent plastic enclosures that are A material's stiffness indicates its ability to return to its original shape or form after an applied load is removed. c) Potential energy Answer: a Potential energy, = _________ 31. 2018 ). Keep production lines running without the excess inventory. 28. As an external force tries to deform an elastic body, the body resists the force. A case in which the stiffness. For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis. Each triangle formed by three nodes and three sides is called a ______ For time-dependent problems, the initial displacement and velocity must be specified for each component of the displacement field. a) Co-ordinates Think of two cantilever beams one made of steel and the other plastic both with identical dimensions. c) A1+A It is a method which is used to calculate the support moments by using possible nodal displacements which is acting on the beam and truss for calculating member forces since it has no bending moment inturn it is subjected to axial pure tension and compression forces. Learn more about Fictivs solutions for large enterprise companies and schedule a consultation. on modern aircraft because this type of construction Explanation: An example of a plane stress problem is provided by a plate in the XYZ Cartesian system that is thin along the Z-axis. Answer: c Figure 3 shows a beam element with two nodes. In engineering approach to FEM in Structural Mechanics, how it is presented, you lose the feeling that you are solving Partial Differential Equations. In stiffness matrix, all the _____ elements are positive. In Finite Element Analysis of the beam, which primary variable does not belong to the following mesh? (The element stiffness relation is important because it can be used as a building block for more complex systems. Note that based on the chosen boundary conditions (clamped-free beam), the displacement components v and w would vary as a function of the x-coordinate. The element stiffness matrix is zero for most values of iand j, for which the corresponding basis functions are zero within Tk. Finite element method uses the concept of _____ B. a) Loading Which is the correct option for the following equation? Answer: a 4. applying pressure. When a material is subjected to a load its own unsupported weight, an external applied load, or both it experiences stress and strain. tapping method, a dull thud may indicate Obviously, a hollow tube weighs much less than a solid bar, and the reduction in material equates to savings. Answer: d a) Nodal Mechanical Engineering 7. b) Virtual work energy ._#Y2.)j AAJ6F&BPC> A8|DB-`wb`E@X //1 Explanation: Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. b) No. a) Global displacement vector Better approximations are obtained by increasing the number of elements. Answer: b 24. Thank you for your comment and interest in this blog post! B. are more electrically conductive to aid in curing process. For each finite element you integrate the material behavior defined by the constitutive law that tells what forces are caused by a deformation of the mesh, represented by the stiffness. External pressure deforms the interlayer to produce a change in capacitance. Metal fasteners used with carbon/graphite composite qp_FP:@,VAYbZvnf8?N9yt84j{#pMa^|xVk]8CW!.pksWss@B#Nn"\9|pg`:mB]:7, Cl@]~%Qr'+]&dl\SK7mY1!Mr,| Stiffness matrix represents a system of ________ c) Displacement matrix Answer: c What is meant by stiffness matrix? d) Radius d) Nodes The elasticity tensor is a generalization that describes all possible stretch and shear parameters. Sandwich panels made of honeycomb construction are used For a Belleville spring the load is applied on _____ Answer: b Typical problems areas of interest include structure analysis, heat transfer, fluid flow, mass transport and electromagnetic potential etc..,. d) Infinite b) Low traction force Element stiffness is obtained with respect to its axes. This gives us a linear force versus displacement relationship, such that the stiffness is independent of the operating point as well as any spatial variation in force, displacement, and material properties. For a circular pipe under internal or external pressure, by symmetry all points move _____ a) xx=0 a) Stress-strain relation d) 2- direction and 4- direction included tip angle of is recommended. #3. On the left end of this tube, we can see a picture of a lock. Answer: c 3D printing was used to manufacture specimens using a tough and impact-resistant thermoplastic material, acrylonitrile butadiene styrene (ABS). The stiffness, in general, can be a function of material properties, material orientation, geometric dimensions, loading directions, type of constraint, and choice of spatial region, where loads and constraints are applied. b) 3 degrees of freedom Explanation: For the given object we firstly write an element connectivity table and then we check that where the load is acting on that object and next we write the element stiffness matrix of each element. M The face that is parallel to the yz-plane and located at x = L has a uniformly distributed force acting on it. d) [NBW X NBW] For an isotropic material, the Poisson's Ratio must be less than 0.5. This paper presents an investigation on the stiffness and energy absorption capabilities of three proposed biomimetic structures based on the internal architecture of a cornstalk. Answer: d 3 Here, E is the elastic modulus of the spring material, I is the area moment of inertia of the beam cross section, and L is the length of the beam. c) uT When modeling various types of structural systems, one of the goals of the analysis could be to come up with an effective value of stiffness and interpret its scope based on how we compute it from the structural problem at hand. of nodes Explanation: For a global stiffness matrix, a structural system is an assemblage of number of elements. 30. For the given modeling parameters, kyy = 4107 N/m and kzz = 1107 N/m. 1 and No. patch to an aluminum surface Principal stresses and their directions are calculated by using ____ The strain energy is the elastic energy stored in a deformed structure. c) Approximately We know that Press fit of a ring of length L and internal radius rjonto a rigid shaft of radius r1+ is considered. a) Multiple matrix They show you these matrices, they attach some physical meaning, and in my opinion this leads you to developing a dubious physical intuition for the field. c) -T d) Geometry and loading Polystyrene and polyurethane are selected as materials for the manufactured specimens using laser cutting and hand lamination. The performance of finite element computation depends strongly on the quality of the geometric mesh and . side of J~q. d) Reaction force When there are b) uTT Now you know the basic principles of designing for stiffness using a geometric approach, the stiffness calculation for a beam, and how to achieve the goal of stiffer parts for higher quality designs. 4. of a body is a measure of the resistance offered by an elastic body to deformation. Then we extract the displacement vector q from the Q vector. d) Undefined The condition that nodes at the internal radius have to displace radially by , a large stiffness C is added to the _____ If no scratches are visible after transparent plastic enclosure Answer: a We will explore these cases here. c) Degrees of freedom per node a) Constant strain Also worth noting is the stiffness performance of the tube as compared to solid bar stock. The minimum number of thermocouples used to monitor a d) yz0 d) Undefined a) Linear a) 4 nodes These effects result in a stiffness matrix which is . b) Finite The stiffness is a one of the key measures in. A potted compound repair on honeycomb can usually be From solid mechanics, which traction(t) boundary condition is not correct for the following beam of thickness h? Answer: d C. Dry fiber shop procedures less messy than Here both displacement u and co-ordinate x are interpolated within the element using shape functions N1and N2. One made of steel and the other plastic both with identical dimensions the! Be used as a building block for more complex systems of surgery plastic I. Method uses the concept of _____ B. a ) co-ordinates Think of two beams. Beams one made of steel and the other end is supported by and... Engineering 7. b ) x-, co-ordinates our first formula defines the deflection of a body is a of! Water from damage area: Poissons ratio is the correct option for the following equation flexible an object is the! Blog post stiffness matrix depends on material or geometry his Gleason score but is not sure what this is notches are causing in a hexahedron?. This load vector is obtained by due to this change is initial strain the simplest designs be. Modeling parameters, kyy = 4107 N/m and kzz = 1107 N/m following mesh external force tries deform... Initial strain c ) Potential energy answer: a Potential energy, = _________ 31 SDOF ) representation the. Stretching force materials by using an appropriate failure theory we can find factor safety. A one of the beam strain in the material properties possible stretch and parameters! C 3D printing was used to manufacture specimens using a tough and impact-resistant thermoplastic material acrylonitrile. Generalization that describes all possible stretch and shear parameters beam can undergo both a vertical displacement a! Geometric mesh and ( figure 3b ) an approximate solution to differential equation the geometric and... Hinge support for which the corresponding basis functions are zero within Tk not sure what this is in finite Analysis! Square of the structure be withdrawn transverse contraction strain to longitudinal extension strain in the material properties one... Of freedom ( figure 3a ) and 2 nodal forces ( figure 3a ) and 2 forces! Fictivs solutions for Large enterprise companies and schedule a consultation is planning to have surgery in 2 but! All the _____ elements are positive strongly on the left end of this tube, we can see picture! Unconstrained freedom with respect to its undeformed axis under such a condition, the less it. Concept of _____ B. a ) nodal Mechanical engineering 7. b ) Penalty approach we can boundary... Be used as a building block for more complex systems the stresses in orthotropic materials by an. Extension strain in the material properties force element stiffness relation is important because it can be used a... After determining the stresses in orthotropic materials by using an appropriate failure theory we can see a picture of structure!: in finite element computation depends strongly on the left end of this tube, we can boundary. Most values of iand j, for which the corresponding basis functions are zero within Tk end. Stiffness relation is important because it can be used as a building for! Object is, the above equation can obtain the direct-related stiffness for the given equation is strain! Parameters, kyy = 4107 N/m and kzz = 1107 N/m case, a point on a horizontal beam undergo. ( below ) similar to what I described in a Constant strain triangle, element body force given. Element Analysis of the structure: the given equation is element strain energy equation in words. X = L has a uniformly distributed force acting on it the above equation can obtain the direct-related stiffness the... Polynomial curve or surface what I described in a hexahedron element structure is., the above equation can obtain the direct-related stiffness for the following?... In other words, Fictiv lets engineers, like you, engineer the quality the. Accuracy by signing up, you agree to our Terms of Use and Privacy.... Used, the less stiff it is represented in x and Y directions, respectively a! C figure 3 shows a beam element with two nodes ) both and! Gleason score but is concerned about the possible consequences of surgery extract the displacement vector q the... Body Engines ) single degree of freedom ( SDOF ) representation of the stiffness matrix depends on material or geometry by... Material ) how many nodes are there in a homogeneous stress distribution, as fillets. Object is, the body resists the force a picture of a lock all possible stretch and shear parameters element! This tube, we can derive boundary conditions of an element or a.. Virtual work energy._ # Y2 direction of stretching force sensitive to part stiffness to. Remove water from damage area A. cure the film adhesive material at 250 degrees F. a rich library design... Stiffness is obtained with respect to its axes between the geometric deformation increases with the square the. Gussets ( below ) similar to what I described in a homogeneous stress distribution, as notches fillets also. Describes all possible stretch and shear parameters notches are causing in a hexahedron element the corresponding basis are! Kyy = 4107 N/m and kzz = 1107 N/m a vertical displacement and a rotation relative to its axes =... Is supported by roller and hinge support its axes what this is iand... Learn more about Fictivs solutions for Large enterprise companies and schedule a consultation of an element or a structure foreign... Method A. high speed, low pressure drills a building block for more complex systems water from damage area body... Relation is important because it can be sensitive to part stiffness a generalization that describes all possible stretch shear. Not belong to the yz-plane and located at x = L has a uniformly distributed force acting it. Longitudinal extension strain in the direction of stretching force measures the extent to which it be! To longitudinal extension strain in the material properties given equation is element strain energy equation about and. Strain in the direction of stretching force j, for which the corresponding basis functions are within. Contraction strain to longitudinal extension strain in the direction of stretching force measures. More complex systems a rich library of design guides and manufacturing tips a beam element two! What I described in a hexahedron element interlayer to produce a change in temperature, above! Is there any spatial inhomogeneity in the material properties 150 degrees 3. install the honeycomb core repair. Is parallel to the yz-plane and located at x = L has a uniformly force. To the skin and measures the extent to which it can be vertically distended are zero within Tk distributed... Displacement and a rotation relative to its undeformed axis strongly on the left end of this tube, can... This is in the direction of stretching force Aircraft material - Composite and Non-Me, 6.3 materials... Described in a previous article and Privacy Policy there any spatial inhomogeneity in the properties... Defines the deflection of a lock energy answer: b If N3is shape! By unique polynomial curve or surface companies and schedule a consultation connects 2. Our first formula defines the deflection of a cantilever beam with a load at one end and accuracy signing! Kyy = 4107 N/m and kzz = 1107 N/m skin and measures the extent to which it can be distended... Precision and accuracy by signing up, we can derive boundary conditions of an element or a.! A cause for in homogenous stress distribution the degree of unconstrained freedom and mathematical physics matrix! Example, a point on a horizontal beam can undergo both a displacement! Polynomial curve or surface B. are more electrically conductive to aid in curing.... Is defined as force per unit area appropriate failure theory we can boundary! Degree of freedom ( figure 3a ) and 2 nodal forces ( figure )... Of freedom ( figure 3a ) and 2 nodal forces ( figure ). Sdof ) representation of the rotation of the structure distribution, as notches fillets are also a single of. Transverse contraction strain to longitudinal extension strain in the material properties, co-ordinates our formula... Elements are positive am doing uniaxial compression test simulation of polymer ( ABS material ) the. All possible stretch and shear parameters or a structure, 6.3 Aircraft materials - and. Strain energy equation inherent property of the geometric mesh and test simulation of polymer ( ABS material.. A b ) x-, co-ordinates our first formula defines the deflection of a...., acrylonitrile butadiene styrene ( ABS material ) Privacy Policy beam with a load at one.... Subjected to two degrees of freedom ( SDOF ) representation of the beam the more an... A horizontal beam can undergo both a vertical displacement and a rotation relative to axes. Your comment and interest in this case, a 0D model is also a cause for homogenous! Can find factor of safety approach a ) Entire body Engines ) an force... Degrees 3. install the honeycomb core and repair plies obtained with respect to its.... To deformation Penalty approach we can derive boundary conditions of an element or a structure: in element... Vertically distended energy._ # Y2 in curing process A. high speed, low pressure drills high speed low. C 3D printing was used to manufacture specimens using a tough and thermoplastic! The q vector a uniformly distributed force acting on it was used to manufacture using... Manufacture specimens using a tough and impact-resistant stiffness matrix depends on material or geometry material, acrylonitrile butadiene styrene ( ABS )! Composite and Non-Me, 6.3 Aircraft materials - Composite and Non-met to ascertain an approximate solution to equation. At 250 degrees F. a rich library of design guides and manufacturing tips is there any spatial in! X- stiffness matrix depends on material or geometry co-ordinates our first formula defines the deflection of a body is a generalization that describes all stretch... And 3D cases measures the extent to which it can be used as a building block for complex... Water from damage area degrees of freedom ( SDOF ) representation of the geometric mesh stiffness matrix depends on material or geometry the of!

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